Question

How can we define the coefficients a half wave symmetry when n is even?

(a) an=0 and bn=0 and a0=0

(b) an=4/T∫x(t)cos(nwt)dt  and bn=0= a0

(c) an=4/T∫x(t)sin(nwt)dt and bn=4/T∫x(t)cos(nwt)dt and a0=0

(d) an=4/T∫x(t)sin(nwt)dt and bn=4/T and a0=0

The question was posed to me during an interview.

Origin of the question is Symmetry Properties of the Fourier Series in portion Fourier Series of Signals and Systems

Answer 1

The correct option is (c) an=4/T∫x(t)sin(nwt)dt and bn=4/T∫x(t)cos(nwt)dt and a0=0

The best explanation: If it is a half wave symmetry then we define the fourier coefficients as-

an=0 and an=4/T∫x(t)cos(nwt)dt and bn=4/T∫x(t)sin(nwt)dt.